{
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     "start_time": "2025-06-28T05:53:04.564788Z"
    },
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   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import torch\n",
    "from torch import nn\n",
    "from d2l import torch as d2l"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "f8a488c1f1cbcf83",
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     "start_time": "2025-06-28T05:53:04.619311Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([1000])\n",
      "torch.Size([1000])\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(None, None)"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
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    "T = 1000\n",
    "time = torch.arange(1, T + 1, dtype=torch.float32)\n",
    "x = torch.sin(0.01 * time) + torch.normal(0, 0.2, (T,))\n",
    "d2l.plot(time, [x], 'time', 'x', xlim=[1, 1000], figsize=(6, 3))\n",
    "print(torch.sin(0.01 * time).shape), print(torch.normal(0, 0.2, (T,)).shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "20e648064c6b0442",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-06-28T05:53:04.757649Z",
     "start_time": "2025-06-28T05:53:04.743509Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([996, 1])\n",
      "torch.Size([996, 4])\n"
     ]
    }
   ],
   "source": [
    "tau = 4  #4步预测，每次取四个点，这样就有996个子序列\n",
    "features = torch.zeros((T - tau, tau))  #采样，样本数，特征\n",
    "for i in range(tau):\n",
    "\tfeatures[:, i] = x[i: T - tau + i]  #拷贝\n",
    "labels = x[tau:].reshape((-1, 1))  #标签就是每一组的下一个标签\n",
    "print(labels.shape), print(features.shape)\n",
    "batch_size, n_train = 16, 600\n",
    "# 只有前n_train个样本用于训练\n",
    "train_iter = d2l.load_array((features[:n_train], labels[:n_train]),\n",
    "\t\t\t\t\t\t\tbatch_size, is_train=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "1a886dc730d229c5",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-06-28T05:53:04.819620Z",
     "start_time": "2025-06-28T05:53:04.807383Z"
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   "outputs": [],
   "source": [
    "# 初始化网络权重的函数\n",
    "def init_weights(m):\n",
    "\tif type(m) == nn.Linear:\n",
    "\t\tnn.init.xavier_uniform_(m.weight)\n",
    "\n",
    "\n",
    "# 一个简单的多层感知机\n",
    "def get_net():\n",
    "\tnet = nn.Sequential(nn.Linear(4, 10),\n",
    "\t\t\t\t\t\tnn.ReLU(),\n",
    "\t\t\t\t\t\tnn.Linear(10, 1))\n",
    "\tnet.apply(init_weights)\n",
    "\treturn net\n",
    "\n",
    "\n",
    "# 平方损失。注意：MSELoss计算平方误差时不带系数1/2\n",
    "loss = nn.MSELoss(reduction='none')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "4ae54013cf10946",
   "metadata": {
    "ExecuteTime": {
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     "start_time": "2025-06-28T05:53:04.867935Z"
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   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch 1, loss: 0.072670\n",
      "epoch 2, loss: 0.056576\n",
      "epoch 3, loss: 0.059488\n",
      "epoch 4, loss: 0.052056\n",
      "epoch 5, loss: 0.050979\n"
     ]
    }
   ],
   "source": [
    "def train(net, train_iter, loss, epochs, lr):\n",
    "\ttrainer = torch.optim.Adam(net.parameters(), lr)\n",
    "\tfor epoch in range(epochs):\n",
    "\t\tfor X, y in train_iter:\n",
    "\t\t\ttrainer.zero_grad()\n",
    "\t\t\tl = loss(net(X), y)\n",
    "\t\t\tl.sum().backward()\n",
    "\t\t\ttrainer.step()\n",
    "\t\tprint(f'epoch {epoch + 1}, '\n",
    "\t\t\t  f'loss: {d2l.evaluate_loss(net, train_iter, loss):f}')\n",
    "\n",
    "\n",
    "net = get_net()\n",
    "train(net, train_iter, loss, 5, 0.01)"
   ]
  },
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   "id": "1258b171f2ea967",
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     "start_time": "2025-06-28T05:53:05.050598Z"
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   "source": [
    "onestep_preds = net(features) #样本带入，进行预测\n",
    "d2l.plot([time, time[tau:]],\n",
    "\t\t [x.detach().numpy(), onestep_preds.detach().numpy()], 'time',\n",
    "\t\t 'x', legend=['data', '1-step preds'], xlim=[1, 1000],\n",
    "\t\t figsize=(6, 3))"
   ]
  },
  {
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   "id": "aaf03676fbf48c6f",
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     "start_time": "2025-06-28T05:53:05.192115Z"
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   "source": [
    "multistep_preds = torch.zeros(T)\n",
    "multistep_preds[: n_train + tau] = x[: n_train + tau]\n",
    "for i in range(n_train + tau, T):\n",
    "\tmultistep_preds[i] = net(\n",
    "\t\tmultistep_preds[i - tau:i].reshape((1, -1))) #这里不给蓝色的点，发现自己的预测的参与下一次预测，错的离谱，因为每一次误差会累计\n",
    "\n",
    "d2l.plot([time, time[tau:], time[n_train + tau:]],\n",
    "\t\t [x.detach().numpy(), onestep_preds.detach().numpy(),\n",
    "\t\t  multistep_preds[n_train + tau:].detach().numpy()], 'time',\n",
    "\t\t 'x', legend=['data', '1-step preds', 'multistep preds'],\n",
    "\t\t xlim=[1, 1000], figsize=(6, 3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "id": "d194929958f237c5",
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    "ExecuteTime": {
     "end_time": "2025-06-28T06:05:34.902852Z",
     "start_time": "2025-06-28T06:05:34.800193Z"
    }
   },
   "outputs": [
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       " <defs>\n",
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       "  </clipPath>\n",
       " </defs>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<Figure size 600x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "max_steps = 64\n",
    "\n",
    "features = torch.zeros((T - tau - max_steps + 1, tau + max_steps))\n",
    "# 列i（i<tau）是来自x的观测，其时间步从（i）到（i+T-tau-max_steps+1）\n",
    "for i in range(tau):\n",
    "\tfeatures[:, i] = x[i: i + T - tau - max_steps + 1]\n",
    "\n",
    "# 列i（i>=tau）是来自（i-tau+1）步的预测，其时间步从（i）到（i+T-tau-max_steps+1）\n",
    "for i in range(tau, tau + max_steps):\n",
    "\tfeatures[:, i] = net(features[:, i - tau:i]).reshape(-1)\n",
    "\n",
    "steps = (1, 4, 16, 64)\n",
    "d2l.plot([time[tau + i - 1: T - max_steps + i] for i in steps],\n",
    "\t\t [features[:, (tau + i - 1)].detach().numpy() for i in steps], 'time', 'x',\n",
    "\t\t legend=[f'{i}-step preds' for i in steps], xlim=[5, 1000],\n",
    "\t\t figsize=(6, 3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "27e4101a1129f303",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-06-28T05:53:05.501250Z",
     "start_time": "2025-06-28T05:53:05.490809Z"
    }
   },
   "outputs": [],
   "source": []
  }
 ],
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  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
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